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arXiv · 1112.1802

Is an irng singly generated as an ideal?

Nicolas Monod·Narutaka Ozawa·Andreas Thom
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Abstract

Recall that a rng is a ring which is possibly non-unital. In this note, we address the problem whether every finitely generated idempotent rng (abbreviated as irng) is singly generated as an ideal. It is well-known that it is the case for a commutative irng. We prove here it is also the case for a free rng on finitely many idempotents and for a finite irng. A relation to the Wiegold problem for perfect groups is discussed.

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Nicolas Monod, Narutaka Ozawa, Andreas Thom. 2012-02-06. Is an irng singly generated as an ideal?. https://doi.org/10.1142/s0218196712500361

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